Abstarct: Lubrication theory has extensive applications in fluid mechanics which one of the most important that is in the field of design bearing types. Studying in this field helps researchers in the design of bearing and determine their best working conditions. Research shows that by adding polymeric materials to mineral oils and changing the behavior of Newtonian fluid to viscoelastic materials lubricant, cause to observe an excellent performance in the lubrication system. Therefore, to study the actual behavior of a viscoelastic lubricant, it was necessary to analyze this problem by applying efficient models in the non-Newtonian field. In the present study, the problem of lubrication for journal and slider bearings was investigated using the nonlinear viscoelastic model of Giesekus and the perturbation theory selected as the solution strategy. The results show that by using a viscoelastic lubricant as a replacement for a Newtonian fluid, make to have a significant increase in the pressure distribution. As a result, cause to increase load capacity on the bearing from the side of the shaft. Another point is that by increasing the mobility parameter and thinning of the fluid in the Gaussian model, we experience a drop in pressure from the viscoelastic fluid on the bearing surfaces. Finally, it is observed that by decreasing the slope and narrowing the crossing space for the flow in the slider bearings, and also by increasing the eccentricity ratio in the journal bearing, the pressure applied by the viscoelastic fluid to the bearing walls increases.